On professional social network sites (like LinkedIn) there are terms like 'recommend someone' or 'endorse someone'. What could be an alternative term that is somewhat lighter in meaning as compared to endorsing someone, but rather more inclined towards meaning 'to appreciate someone in academic or professional context or to appreciate his works'?

I don't know the context you are going for, so maybe too lighthearted, but if you're leaning away from the "endorse" or "vouch for" idea, maybe you just want something that casually indicates that we could/did hang out together such as, "High Fives" or "Lunches with."